Download CP Geometry Midterm Review Packet - Hatboro

CP Geometry Midterm Review Packet
Name:_________________
Date:_______________
True or False:
1._______ Every line segment has one and only one midpoint.
2. ______ If two angles are equal, they are right angles.
3. ______ If two angles are supplementary, then they are equal.
4. ______ Two points determine one and only one plane.
5. ______ An angle has one and only one bisector.
6. ______ The sum of two acute angles is an obtuse angle.
7. ______ If a triangle is equilateral, then it is isosceles.
8. ______ Since the sum of 20°, 30°and 40° is 90°, then the angles are
complementary.
9. ______ Every polygon has more than three sides.
10. ______ The sum of the interior and exterior angles of a pentagon are
the same.
Set up and solve the following word problems.
11. Two angles are supplementary. Find the angles if one angle is 45°more
than twice the other angle.
12. Two angles are complimentary. If one angle is 32° less than the other,
Find the angles.
13. Two angles are supplementary. Find the angles if one angle is 10°more
than two- thirds the other angle.
14. In a triangle, <B is 12° larger than <A. <C is equal to the sum of the first
two angles. Find the angles.
15. ΔABC is isosceles and one of the base angles is 15° larger than the
vertex angle. Find the angles.
16. In a triangle, <B is 2 times as large as <A. If <C is 4° less than <A, find all
three angles.
17. Find the sum of the interior angles of a heptagon.
18. Find the number of degrees in each exterior angle of a regular octagon.
19. How many sides does a polygon have if the sum of its interior angles is
1800°?
20. How many sides does a regular polygon have if each interior angle is
144°?
Solve the following angle problems:
21.
< BED = 52°
< CED = 28°
< AEB = 18°
Find < AEC_________________
A
B
C
D
E
22.
EB bisects < AED
< AED = 74°
< BEC = 19°
Find < CED___________________
A
B
C
D
E
23.
< AEB = 29° 14’
< CED = 31° 26’
< BEC = 24° 34’
Find < AED____________
A
B
C
E
D
24.
BC bisects < ABD
< ABD = 71° 38’
Find < CBD_____________
A
C
B
D
25.
(BE Bisects < ABC)
< ABD = 56°
< DBC = 28°
Find < ABE________________
<
A
E
D
B
C
26.
< ABE = 83° 14’
< ABC = 23° 48’
< CBD = 27° 17’
Find < DBE = ____________
A
C
D
B
E
27. ∆ABC is isosceles with base AC.
m< A = 3x
m< B = 4x
Find x = ______
m< A= _______
m< B = _____
m< C=_____
B
A
C
28. ΔABC is isosceles with base AC.
m< BCD = 110°
Find m< A _______ m< B ________
m< ACB________
B
A
C
D
Draw the segment and then solve.
29. B is the midpoint of AC .
AC = x + 3
AB = x
AC = _____
AB = _____
BC = _____
30.
AC = _____
AB = _____
BC = _____
B is between points A and C.
AB = 4x – 1
BC = 2x + 3
AC = 8x
31. Find the sum of the measures of the interior angles of a 11-gon.
_______________
32. The measure of each exterior angle of a polygon is 45o. Find the
number of sides of the polygon.
_______________
33. Find the measures of an interior and exterior angle of a regular
pentadecagon.
_______________
34. The measure of an interior angle of a regular polygon is 120o. Find the
number of sides of the polygon.
_______________
35. If the exterior angle of a regular polygon measures 36o, find the sum of
the measures of the interior angles.
_______________
36. If the measure of each of the interior angles of a regular polygon is 100
more than the measure of each of the exterior angles, name the polygon.
______________
37. The sum of the interior angles of a polygon are 900o. Name the polygon.
_______________
38. The measures of the interior angles of a pentagon are x, 3x, 2x – 1,
6x – 5, and 4x + 2. Find the measure of each angle.
39. Δ DOG ≈ Δ __________ BY:____________________
C
D
A
O
G
T
40. Δ BID ≈ Δ____________
I
B
D
R
BY:____________________
41. Δ SAN ≈ Δ____________
S
BY:____________________
N
A
E
K
42. Δ GTA ≈ Δ____________
BY:____________________
G
O
T
A
43. Δ ABD ≈ Δ____________
Given < ADB ≈ < CDB
A
D
C
B
BY:____________________
44. Δ ABC ≈ Δ____________
BY:____________________
D
A
C
E
B
Use the following sketch to solve:
C
A
B
E
F
D
H
G
45. < ABF = 6x – 16
< BFH = 2x +28
Find X _____________
46. < DBF = 5x + 16
< BFH = 3x + 12
Find X______________
< EFB___________ < CBD____________
< ABF___________
< EFB___________
Solve:
47. If two lines are parallel and are cut by a transversal, two alternate
interior angles represented by 3x and 5x – 70. Find the angle measures.
48. If two lines are parallel and are cut by a transversal, two corresponding
Angles represented by 2x + 10 and 4x -50. Find the angle measures.
49. If two lines are parallel and are cut by a transversal, two same side
interior angles represented by 2x and 3x. Find the angle measures.
Use the following sketch for # 50 – 55.
A
E
G
7
5
8
F
6
3
1
B
4
2
C
D
H
50. List all Alternate Interior angles._____________________________
51. List all Alternate Exterior angles._____________________________
52. List all Corresponding angles.________________________________
53. List all Same side interior angles._____________________________
54. If < ABC = 108° then < GFH =_______; < HFB=_________________
55. If < DBF = 95°, then < BFH=________; < BFE=__________________
A
56.
B
I
E
D
C
G
F
57.
AB CE FH
ABD  32
BDG  89
EDG  _________
DGH  _________
H
E
F
A
AB CD
BFG  _________
FGD  _________
B
5x+16
G 3x+12
C
D
H
E
58. AB || CD
<AFG = __________
<FGD = __________
A
B
F
6x - 16
G
C
2x +28
D
H
A
E
59. BF || CD
EC bisects <ACD
<EGF = 42°
< CBF = __________
< ABG = _________
B
C
G
F
D
Simplify each radical expression
60.
61.
4 600
17
3
62.
4 96  2 54
Set up the following ratio and reduce to lowest terms.
63. 10 inches to 3 feet
___________________
64. 30 minutes to 5 hours
___________________
65.
___________________
5 3
to
27
Solve the proportion.
66.
7 9

x 27
67.
4 3 2

3
x
68.
16 x

x 4
69.
7 5
x

2 5 8 5
Are the triangles similar? If so, write a similarity statement and
identify the postulate or theorem that justifies your answer.
70.
A
D
G
92°
68°
23°
C
T
92°
O
71.
10
S
L
N
8
6
15
M
72.
A
B
12
20
B
25
Z
24
Y
32°
44
A
9
C
32°
X
Use the given information to determine the similar triangles. Then,
solve for the missing side.
73. Given AG
YM.
Y
RA = 5
AG = 6
YM = 15
Find RM = ____
A
R
G
74. Given AB
A
M
DE.
B
AB =
C
AC =
2 5
4 3
ED =
5 6
Find CD = ________
D
E
75. Find x and y in the diagram below if EB
DC.
D
DC = 27
AD = 33
AB = 20
AC = 30
E
x
Find x = _____
Find y = _____
y
A
B
C
76. If ABC ~ QPR , m < A = 30° and m < B = 97°, find the measures of
angles Q, P, and R.
m < Q = _____
m < P = ______
m < R = ______
77.-79 Use the diagram at the right to the answer the next 3 questions.
77. If AB=3x+8 and GJ=2x+24, what is AB? __________
78. If AC=3y-5 and HJ=4y+2, what is HB? __________
79. If GH=7z-1 and BC=4z-3, what is GH? __________
80-83. Is this triangle possible?
9. 2.5, 3.5, 5 ___________
10. 2, 6, 9 __________
11. 9, 12, 15 _________
84-85. Find the third side. Write an inequality statement.
84. 5, 15, ___________________
86-87 Find the missing angles.
86.
85. 8, 22, __________________
87.
88-91 Use the diagram to the right.
88. If AB=BC, and m B=75, then the longest side is ____________.
89. If m A=90, then the longest side is ______________.
90. If AB=8, BC=6 and AC=13, then the largest angle is ______.
91. If AB=5, BC=7, and AC=10, then the smallest angle is ________.